Ok, so I have now been able to use the 7.0 battle window. I was not able to use multiplex tracking, but was able to get through the first round of combat. One of the functions of the Battle Window is to keep track of what ships have fired in a given tactical round,

When both sides finished firing, I pressed "Next turn", thinking it would allow me to start the next tactical turn of fighting. I set up a new attack, finished the attack, but the "fired" column did not advance, like it did during the first round of battle.

Ok, so I have now been able to use the 7.0 battle window. I was not able to use multiplex tracking, but was able to get through the first round of combat. One of the functions of the Battle Window is to keep track of what ships have fired in a given tactical round,

When both sides finished firing, I pressed "Next turn", thinking it would allow me to start the next tactical turn of fighting. I set up a new attack, finished the attack, but the "fired" column did not advance, like it did during the first round of battle.

What should I do?

It's been a long time since I used this

I setup a quick battle though and it seems to be working fine as far as I can tell. I fired a few times on turn 1 and the firing ships showed 1, the current turn number, in the Fired column. I then pressed next turn so I was on Turn 2. When I fired again, the number in the fired column for those ships changed to 2. What is happening differently in your game?

If you want to use multiplex tracking (i.e. fire at more than one enemy ship), then after you press Setup Fire and the AWR pops up, just change the number of weapons you are firing. The select a second target and change the number of weapons again. This way you can split your fire against multiple targets.

Thanks for the info on multiplexing. I think the issue for me on advancing the battle timer is that I had to make sure that all fleets had fired, whether they were in the battle or not. (Some of the enemy fleets were in the same strategic hex, as it was their home system). One thing that did happen is that ships that had been damaged were repaired all the way, so now I have to reset that damage before starting the second round of battle. Thank God for starting this battle on paper (which is where the damage is recorded)!

Well, I have decided to restart this scenario, and now I can answer my own question about resetting the firing turn count. Under the tab at the top 'Fleet Activation Status' (I could not see earlier as the color was light yellow against gray background), there is a dropdown box saying 'reset fleet 1 (or 2) to zero. Thus I can renew the battle after regrouping, re-arming, sending beat-up ships back through the WP, etc., and then have a new firing count.